Question

the crankshaft of an engine increases its spin from 1,000 to 2,000 rpm in 0.50 s what is its angular acceleration

Answer 1

Answer:

angular acceleration = 209.44 [rad/s^2]

Explanation:

First we have to convert the velocities which are in revolutions per minute to radians on second.

where:

$w_{0} = 1000 [\frac{rev}{min}]*[\frac{2\pi rad }{1rev}] * \frac{1min}{60s} = 104.7[\frac{rad}{s} ]\\w = 2000 [\frac{rev}{min}]*[\frac{2\pi rad }{1rev}] * \frac{1min}{60s} = 209.4[\frac{rad}{s} ]$

Now we can find the angular acceleration:

$w=w_{0} + \alpha *t\\\alpha =\frac{w-w_{0} }{t} \\\alpha =\frac{209.43-104.71}{\0.5 } \\\alpha = 209.44[\frac{rad}{s^{2} } ]$